Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion

We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state, are exactly determined as a series expansion in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of this analyticity property is discussed.Comment: 26 pages, 5 figure

Exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by the system during its evolution are distributed according to a multinomial probability density. The class includes i) the uniformly fully connected models, namely a collection of states all connected with equal hopping coefficients and in the presence of a potential operator with arbitrary levels and degeneracies, and ii) the random potential systems, in which the hopping operator is generic and arbitrary potential levels are assigned randomly to the states with arbitrary probabilities. For this class of models we find a universal thermodynamic limit characterized only by the levels of the potential, rescaled by the ground-state energy of the system for zero potential, and by the corresponding degeneracies (probabilities). If the degeneracy (probability) of the lowest potential level tends to zero, the ground state of the system undergoes a quantum phase transition between a normal phase and a frozen phase with zero hopping energy. In the frozen phase the ground state condensates into the subspace spanned by the states of the system associated with the lowest potential level.Comment: 31 pages, 13 figure

Shell Model of Two-dimensional Turbulence in Polymer Solutions

We address the effect of polymer additives on two dimensional turbulence, an issue that was studied recently in experiments and direct numerical simulations. We show that the same simple shell model that reproduced drag reduction in three-dimensional turbulence reproduces all the reported effects in the two-dimensional case. The simplicity of the model offers a straightforward understanding of the all the major effects under consideration

Experimental test of the no signaling theorem

In 1981 N. Herbert proposed a gedanken experiment in order to achieve by the ''First Laser Amplified Superluminal Hookup'' (FLASH) a faster than light communication (FTL) by quantum nonlocality. The present work reports the first experimental realization of that proposal by the optical parametric amplification of a single photon belonging to an entangled EPR pair into an output field involving 5 x 10^3 photons. A thorough theoretical and experimental analysis explains in general and conclusive terms the precise reasons for the failure of the FLASH program as well as of any similar FTL proposals.Comment: 4 pages, 4 figure

Quantum Information and Wave function Collapse

Inofrmation-theoretical restrictions on information transferred in the measurement of object S by information system O are studied. It is shown that such constraints, induced by Heisenberg commutation relations, result in the loss of information about the purity of S state. Consequently, it becomes impossible for O to discriminate pure and mixed S states. In individual events this effect is manifested by the stochastic outcomes of pure S state measurement, i.e. the collapse of pure S state.Comment: 8 pages, talk given on Simposium 'Frontiers of fundamental Physics', Udine, Italy, January 2008, to appear in Proceeding

Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths

Using a hydrodynamic approach we examine bulk- and surface-induced second and third harmonic generation from semiconductor nanowire gratings having a resonant nonlinearity in the absorption region. We demonstrate resonant, broadband and highly efficient optical frequency conversion: contrary to conventional wisdom, we show that harmonic generation can take full advantage of resonant nonlinearities in a spectral range where nonlinear optical coefficients are boosted well beyond what is achievable in the transparent, long-wavelength, non-resonant regime. Using femtosecond pulses with approximately 500 MW/cm2 peak power density, we predict third harmonic conversion efficiencies of approximately 1% in a silicon nanowire array, at nearly any desired UV or visible wavelength, including the range of negative dielectric constant. We also predict surface second harmonic conversion efficiencies of order 0.01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects. These remarkable findings, arising from the combined effects of nonlinear resonance dispersion, field localization, and phase-locking, could significantly extend the operational spectral bandwidth of silicon photonics, and strongly suggest that neither linear absorption nor skin depth should be motivating factors to exclude either semiconductors or metals from the list of useful or practical nonlinear materials in any spectral range.Comment: 12 pages, 4 figure

Exact Monte Carlo time dynamics in many-body lattice quantum systems

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model

Screening and attraction of dust particles in plasmas.

The potential around a dust particle in a plasma is found using the collisional hydrodynamic equations of dusty plasmas, taking into account ion-dust and ion-neutral collisions and considering the plasma source proportional to the dust density. The linear screening is strongly influenced by the collisions and can substantially differ from Debye screening. Attraction of negatively charged dust particles can occur due to overscreening by the ion fluxes in the presence of friction forces